Q:
# How Do You Use a Formula for Angles in a Triangle?

**Three laws can be used to find the sides and angles of almost any triangle: the Law of Angles, the Law of Sines, and the Law of Cosines.** The Law of Angles means that all three angles of a triangle add up to 180 degrees. The Law of Sines is that the ratio of each side to the sine of its opposite angle is equal: a/sin(A) = b/sin(B) = c/sin(C). The Law of Cosines works when all sides are known.

If the only quantities you know are angles, the triangle cannot be solved because you need to know at least one of the sides. The equation for the Law of Cosines is c^2 = a^2 + b^2 - 2abcos(C). By substituting the values for the sides and taking the inverse cosine, you can derive the angle opposite side c and proceed from there. C is usually the longest side, but not always. As an example, assume you have a triangle with sides 3. 4 and 5. Substituting these values yields 5^2 = 3^2 + 4^2 - 2(3)(4)cos(C), or 25 = 9 + 16 - 24cos(C). By solving and taking the inverse cosine, you can determine that one of the angles is 90 degrees.

Learn more about Shapes-
Q:
## What Are Some Geometry Formulas for Triangles?

A: A triangle is a three-sided polygon where the sum of its interior angles equals 180 degrees. Some common formulas for triangles include perimeter, the tota... Full Answer >Filed Under: -
Q:
## How Many Degrees Does an Equilateral Triangle Have?

A: The sum of the interior angles of an equilateral triangle equals 180 degrees. This stems from the fact that the combined interior angles of any given trian... Full Answer >Filed Under: -
Q:
## What Are the 30-60-90 Triangle Rules?

A: A 30-60-90 triangle has interior angles equal to 30, 60 and 90 degrees. This is always a right triangle with the 90-degree angle located opposite the longe... Full Answer >Filed Under: -
Q:
## What Is an Isosceles Triangle?

A: An isosceles triangle is a specific type of triangle where only two of the side lengths and two of the internal angles are equal. There are also other type... Full Answer >Filed Under: